Average Error: 0.3 → 0.2
Time: 13.1s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[x + \left(z \cdot \left(y - x\right)\right) \cdot 6\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
x + \left(z \cdot \left(y - x\right)\right) \cdot 6
double f(double x, double y, double z) {
        double r53166119 = x;
        double r53166120 = y;
        double r53166121 = r53166120 - r53166119;
        double r53166122 = 6.0;
        double r53166123 = r53166121 * r53166122;
        double r53166124 = z;
        double r53166125 = r53166123 * r53166124;
        double r53166126 = r53166119 + r53166125;
        return r53166126;
}
↓
double f(double x, double y, double z) {
        double r53166127 = x;
        double r53166128 = z;
        double r53166129 = y;
        double r53166130 = r53166129 - r53166127;
        double r53166131 = r53166128 * r53166130;
        double r53166132 = 6.0;
        double r53166133 = r53166131 * r53166132;
        double r53166134 = r53166127 + r53166133;
        return r53166134;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.3

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]

  2. Taylor expanded around inf 0.2

    \[\leadsto x + \color{blue}{\left(6 \cdot \left(z \cdot y\right) - 6 \cdot \left(x \cdot z\right)\right)}\]

  3. Simplified0.2

    \[\leadsto x + \color{blue}{\left(z \cdot \left(y - x\right)\right) \cdot 6}\]

  4. Final simplification0.2

    \[\leadsto x + \left(z \cdot \left(y - x\right)\right) \cdot 6\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))